Equity return predictability, time varying volatility and learning about the permanence of shocks

I consider a consumption based asset pricing model where the consumer does not know if shocks to dividends are stationary (temporary) or non-stationary (permanent). The agent uses a Bayesian learning algorithm with a bias towards recent observations to assign probability to each process. While the true process is stationary, the consumer’s beliefs change as he misinterprets a drift in dividends from their steady state value as an increased likelihood that the dividend process is non-stationary. Belief changes result in large swings in asset prices which are subsequently reversed. The model then is consistent with a broad array of asset pricing puzzles. It predicts the negative correlation between current returns and future returns and the PE ratio and future returns. Consistent with the data, I also find that consumption growth negatively correlates with future returns and the PE ratio and consumption growth forecast future consumption growth. The model amplifies return volatility over the benchmark rational expectations case and exactly matches the standard deviation of consumption. Finally, the model generates time varying volatility consistent with the data on quarterly equity returns.